I want to go in and get a butler in my current play through to see if this is happening in my game. I've never had a butler die unless I did it lol. Maybe it's a recent thing?
To make them work for me... I usually praise them whenever they do good. I often check them in CAS and make them over a bit and sometimes even give them better traits depending on what type of story I want from them. I don't depend on the the Nanny or Butler to autonomously take care of kids even though often they will. I actually play the kids and ask them to do things. Like feed them, potty train them, use flash cards with them, read to them ect. They get better at doing things after they are trained some.